Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17989496 | C2 | semidirect |
| 2. C2×#17989494 | C2 | semidirect |
| 3. #22625060 | C2 | semidirect |
| 4. #22625058 | C2 | semidirect |
| 15. #17988979 | C4 | semidirect |
| 17. #17988974 | C4 | semidirect |
| 21. C4×#11924012 | C4 | semidirect |
| 22. #532×C73 | C4 | semidirect |
| 50. #14556502 | C2×C4 | semidirect |
| 51. #14556502 | C2×C4 | semidirect |
| 54. C4⋊Q8×C73 | C2×C4 | semidirect |
| 55. #127×C73 | C2×C4 | semidirect |
| 182. C73 | #13578 | semidirect |
| 185. #532 | #64408 | semidirect |
| 217. C4⋊Q8 | C2×#64408 | semidirect |
| 218. #127 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989496 | 2 |
| C2×#17989494 | 2 |
| #22625060 | 2 |
| #22625058 | 2 |
| #22620399 | 2 |
| #13578 | 73 |